Block 2
Polynomials Introduction
What is to be learned?
• What a poLynomial is
• How you know what degree a poLynomial
is
• What the big L is, and how it w...
Spot The PoLynomial
x2
+ 4x – 2
7x + 2
sinx
5x2
-6x7
8x





degree 2
degree 7
degree 1
A Calculation
f(x) = 3x4
– 2x3
+ x2
– 4x + 7
f(2)?
= 3(2)4
– 2(2)3
+ 22
– 4(2) + 7
= 35
Causes a lot of tension
Introducing the Big L
f(x) = 3x4
– 2x3
+ x2
– 4x + 7 f(2)?
3 -2 1 -4 7
Introducing the Big L
f(x) = 3x4
– 2x3
+ x2
– 4x + 7 f(2)?
3 -2 1 -4 72 3
X
2
6
+
4
X
2
8
+
9
X
2
18
+
14
X
2
28
+
35
Introducing the Big L
f(x) = 3x4
– 2x3
+ x2
– 4x + 7 f(2)?
3 -2 1 -4 72 3
X
2
6
+
X
2
8
+
X
2
18
+
X
2
28
+
353
f(2) = 35
...
Introducing the Big L
f(x) = 4x4
– 5x3
+ 2x2
– 3x + 11 f(3)?
-5 2 -3 113 4
12
7
21
23
69
66
198
2094
f(3) = 209
PoLynomials
• Expressions with (non negative) powers of x
• Highest power gives the
• PoLynomial calculations invariably i...
Calculating Function Values
With The Big L
f(2)? f(x) = 3x4
– 4x3
+ x2
– 2x + 9
3 -4 1 -2 92
X
2
6
+
2
X
2
4
+
5
X
2
10
+
...
Key Question
f(x) = 2x4
– 6x3
+ 5x2
– 4x + 16 f(3)?
-6 5 -4 163 2
6
0
0
5
15
11
33
492
f(3) = 49
Beware
3x4
+ 2x2
– 7x + 9
3 2 -7 9
no x3
term
0
of 12

Polynomials intro

Polynomials Intro
Published on: Mar 4, 2016
Published in: Education      
Source: www.slideshare.net


Transcripts - Polynomials intro

  • 1. Block 2 Polynomials Introduction
  • 2. What is to be learned? • What a poLynomial is • How you know what degree a poLynomial is • What the big L is, and how it works
  • 3. Spot The PoLynomial x2 + 4x – 2 7x + 2 sinx 5x2 -6x7 8x      degree 2 degree 7 degree 1
  • 4. A Calculation f(x) = 3x4 – 2x3 + x2 – 4x + 7 f(2)? = 3(2)4 – 2(2)3 + 22 – 4(2) + 7 = 35 Causes a lot of tension
  • 5. Introducing the Big L f(x) = 3x4 – 2x3 + x2 – 4x + 7 f(2)? 3 -2 1 -4 7
  • 6. Introducing the Big L f(x) = 3x4 – 2x3 + x2 – 4x + 7 f(2)? 3 -2 1 -4 72 3 X 2 6 + 4 X 2 8 + 9 X 2 18 + 14 X 2 28 + 35
  • 7. Introducing the Big L f(x) = 3x4 – 2x3 + x2 – 4x + 7 f(2)? 3 -2 1 -4 72 3 X 2 6 + X 2 8 + X 2 18 + X 2 28 + 353 f(2) = 35 4 9 14
  • 8. Introducing the Big L f(x) = 4x4 – 5x3 + 2x2 – 3x + 11 f(3)? -5 2 -3 113 4 12 7 21 23 69 66 198 2094 f(3) = 209
  • 9. PoLynomials • Expressions with (non negative) powers of x • Highest power gives the • PoLynomial calculations invariably involve The Big L (also known as nested calculation scheme) (by those with a sad lack of imagination) degree
  • 10. Calculating Function Values With The Big L f(2)? f(x) = 3x4 – 4x3 + x2 – 2x + 9 3 -4 1 -2 92 X 2 6 + 2 X 2 4 + 5 X 2 10 + 8 X 2 16 + 253 f(2) = 25
  • 11. Key Question f(x) = 2x4 – 6x3 + 5x2 – 4x + 16 f(3)? -6 5 -4 163 2 6 0 0 5 15 11 33 492 f(3) = 49
  • 12. Beware 3x4 + 2x2 – 7x + 9 3 2 -7 9 no x3 term 0